It is the first code with an explicit construction to provably achieve the channel capacity for symmetric binary-input, discrete, memoryless channels (B-DMC) with polynomial dependence on the gap to capacity.
[1] Polar codes were developed by Erdal Arikan, a professor of electrical engineering at Bilkent University.
Notably, polar codes have modest encoding and decoding complexity O(n log n), which renders them attractive for many applications.
Moreover, the encoding and decoding energy complexity of generalized polar codes can reach the fundamental lower bounds for energy consumption of two dimensional circuitry to within an O(nε polylog n) factor for any ε > 0.
Primarily, the original design of the polar codes achieves capacity when block sizes are asymptotically large with a successive cancellation decoder.
Polar performance can be improved with successive cancellation list decoding, but its usability in real applications is still questionable due to very poor implementation efficiencies caused by the iterative approach.
The improvements have been introduced so that the channel performance has now almost closed the gap to the Shannon limit, which sets the bar for the maximum rate for a given bandwidth and a given noise level.
[4] In November 2016, 3GPP agreed to adopt polar codes for the eMBB (Enhanced Mobile Broadband) control channels for the 5G NR (New Radio) interface.
The weights of these NNs are determined by estimating the mutual information of the synthetic channels.
The computational complexity of NPDs is determined by the parameterization of the neural networks, unlike successive cancellation (SC) trellis decoders,[15] whose complexity is determined by the channel model and are typically used for finite-state channels (FSCs).
[17] This flexibility allows NPDs to be used in various decoding scenarios, improving error correction performance while maintaining manageable computational complexity.